A challenging logic problem involving five criminals charged with five
crimes. The names of the criminals are the same as the crimes, but no
criminal commited the crime of his name. Using several clues,
determine who committed murder.

A student of syllogisms gets thrown by statements that seem out of order. She and
Doctor Peterson discuss biconditionality, canceling, plumbing -- even
gibberish -- until order and letters give way to the more fundamental substrate of logic: relationships.

Let X={1,2,3,4,5}, Y={3,4}. Define a relation R on the power set of X by
A R B if A U Y = B U Y. Prove that R is an equivalence relation. What is
the equivalence class of {1, 2}? How many equivalence classes are there?